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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 65520.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.o1 | 65520m4 | \([0, 0, 0, -1320843, -583600358]\) | \(170694618101416082/231440493375\) | \(345538805084928000\) | \([2]\) | \(884736\) | \(2.2705\) | |
| 65520.o2 | 65520m3 | \([0, 0, 0, -990363, 376607338]\) | \(71953090392723122/599853515625\) | \(895576500000000000\) | \([2]\) | \(884736\) | \(2.2705\) | |
| 65520.o3 | 65520m2 | \([0, 0, 0, -105843, -3559358]\) | \(175663952372164/94325765625\) | \(70413806736000000\) | \([2, 2]\) | \(442368\) | \(1.9239\) | |
| 65520.o4 | 65520m1 | \([0, 0, 0, 25377, -436322]\) | \(9684496745264/6045141375\) | \(-1128168463968000\) | \([2]\) | \(221184\) | \(1.5774\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.o have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.o do not have complex multiplication.Modular form 65520.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
